K-stiffness Method Research Articles

Influence of secondary reinforcements on the behavior of geosynthetic reinforced soil walls

This paper presents numerical simulations to investigate the influence of secondary reinforcements on the behavior of geosynthetic reinforced soil (GRS) walls under static loading. Simulations were conducted using a finite difference program to model an instrumented field GRS wall with secondary reinforcements. Simulated results are in good agreement with field measurements, including facing displacements, lateral soil stresses, and tensile strains of the primary and secondary reinforcement. A parametric study was then conducted to investigate the influences of secondary reinforcement length, backfill soil friction angle, and wall height on the static behavior of GRS walls with secondary reinforcements. Results indicate that the maximum facing displacement and the required reinforcement tensile force of primary reinforcements generally decrease with increasing secondary reinforcement length up to a critical value. The decreasing effect is more pronounced for GRS walls with lower soil friction angle and higher wall height. The K-stiffness method is overconservative for the calculation of required tensile force of primary reinforcements for GRS walls with secondary reinforcements, and the overestimation increases with increasing secondary reinforcement length. A design method that accounts for the influence of secondary reinforcements on the internal stability of GRS walls is provided.

Full-scale mechanically stabilized earth (MSE) walls under strip footing load

This study analyses two full-scale model tests on mechanically stabilized earth (MSE) walls. One test was conducted with a rigid and one with a flexible wall face. Other parameters were the same in these two tests, like the number and type of geogrid layers, the vertical distance between the layers and the soil type. The loads and strains on the reinforcement are measured as function of the horizontal and vertical earth pressure and compared with analytical models. Specifics regarding the behavior of the geogrids under the compaction load during the construction of the model and under strip footing load are included in the study. Results are compared with AASHTO and the empirical K-stiffness method. In this study, an analytical method is developed for the MSE walls taking into account the facing panel rigidity both after backfill construction and after strip footing load. There is good agreement between the proposed analytical method and the experimental results considering the facing panel rigidity. The results indicate that the tensile force on reinforcement layers for rigid facing is less than the flexible facing. The maximum strains in the reinforcement layers occurred in the upper layers right below the strip footing load. The maximum wall deflection for the flexible facing is more than for the rigid facing. The maximum deflection was at the top of the wall for the rigid facing and occurred at z/H = 0.81 from top of the wall for the flexible facing.

A Mechanistic Pullout Model for GRS Walls Under Kinematic Consideration

This paper presents a modified mechanistic model to study the pullout responses of geosynthetic reinforced soil walls. The analysis considers the kinematics of the failure, the stiffness and the deformation compatibility of the reinforcement. An updated discretization technique is proposed to account for the deformation compatibility of the reinforcement. A simple iteration scheme is suggested to compute the active length of the reinforcement, which is essential for the before pullout response of an extensible reinforcement. The analysis is performed using a linear-elastic subgrade based on Pasternak model and the resulting second order differential equations in nondimensionalized form are solved applying the finite difference method with the proper boundary conditions. A case study is conducted for a series of full-scale instrumented reinforced soil walls to validate the present analysis. The reinforcement load at each level was back-predicted using the present analysis, and the results are compared with the measured data, AASHTO simplified method and K-stiffness method. The back-analysis demonstrates that the present analysis can be readily integrated with the existing method of analysis (AASHTO) and gives a better prediction of the reinforcement load. A parametric study is also conducted to quantify, predominantly the effect of reinforcement stiffness on the pullout response. The pullout is found to be the prevalent mode of failure for higher reinforcement stiffness; however, for a lower stiffness, the strain may exceed the allowable limit causing a tension failure before the pullout.

Improved Simplified Method for Prediction of Loads in Reinforced Soil Walls

AbstractThe Simplified Method as reported in AASHTO and Federal Highway Administration (FHWA) manuals has been demonstrated to give poor predictions of unfactored reinforcement loads and strains, especially for geosynthetic reinforced soil walls. The writers have proposed the K-stiffness Method to improve the load prediction accuracy for walls under working stress (operational) conditions. However, it has also been recognized in recent publications by the writers and others that further improvements to the K-stiffness Method are needed. Furthermore, acceptance of the K-stiffness Method has been hindered due to its perceived complexity and the use of the plane strain friction angle to quantify the strength of the reinforced soil. This paper takes a fresh look at both methods and uses lessons learned from the K-stiffness Method development to improve the accuracy of the AASHTO/FHWA Simplified Method. Key parameters introduced during the development of the K-stiffness Method are applied to the Simplified Met...

Modeling of the compaction-induced stress on reinforced soil walls

A new simple analytical procedure (AASHTO modified) that includes the effect of the induced stress due to backfill compaction for use with conventional design methods of geosynthetic reinforced soil (GRS) walls is proposed. The proposed analytical procedure may be used with any conventional design methods that do not take into consideration the effect of the compaction-induced stress in their calculations. This approach is based on an equation suggested by Wu and Pham (2010) to calculate the increase in lateral stress in a reinforced soil mass due to compaction. Additionally, two numerical procedures for modeling of compaction are described. Analyses using these procedures were performed to evaluate the capability of the proposed analytical procedure. The results were compared with values predicted using the Ehrlich and Mitchell (1994) method, the modified version of the K-stiffness method (Bathurst et al., 2008) and the AASHTO simplified method. The results show that the AASHTO modified method and the numerical analyses, in which the compaction-induced stress was modeled using two distributed loads at the top and bottom of each soil layer, resulted in values of the maximum reinforcement tension, Tmax, that agree with those from the full-scale test and those calculated by Ehrlich and Mitchell (1994). On the other hand, the K-stiffness method under-predicts the measured Tmax values. Moreover, numerical modeling of compaction using a distribution load only at the top of each soil layer overestimated the measurements.

Analyses of reinforced embankment on soft and hard foundations

In this paper, the analyses and design using conservative limit equilibrium methods (AASHTO simplified and FHWA structure stiffness methods) were compared with the working stress methods called K-stiffness method (original and modified K-stiffness methods). Moreover, the predictions from the K-stiffness methods were confirmed from the observed data for a reinforced embankment on a hard foundation. Furthermore, since the reinforcement loads increased due to post-construction settlements for reinforced embankments on soft foundation, a further modification of the K-stiffness method is proposed. This further modification is concerned with the proposed settlement factor (Φs). The validity of this further modification is demonstrated by the good agreement between the maximum measured reinforcement loads and the recalculated maximum reinforcement loads from further modified K-stiffness method.

Performance of an 11 m high block-faced geogrid wall designed using the K-stiffness method

An 11 m high dry-stacked masonry concrete block wall reinforced with a high-density polyethylene (HDPE) geogrid was designed, instrumented, and monitored for a period of 2 years as part of a highway-widening project southeast of Seattle, Washington, in the USA. An extensive materials-testing program was conducted to characterize the geogrid and backfill soil properties. The empirical-based K-stiffness method was used to design the wall, and this approach resulted in a 35% reduction in total required reinforcement strength compared with the American Association of State Highway and Transportation Officials / Federal Highway Administration (AASHTO/FHWA) simplified method. The cost savings more than compensated for the cost of the instrumentation program. Geogrid strains were measured using strain gauges and extensometers, and the walls were surveyed to monitor facing deformations. The stiffness of the geogrid materials was computed from the results of laboratory in-isolation constant-load (creep) tests. The time- and strain-dependent stiffness values, in combination with measured strains, were used to compute measured reinforcement loads at the reinforcement connections and at locations within the reinforced soil backfill. The measured loads were compared with class A, B, and C1 predictions using the AASHTO/FHWA simplified and K-stiffness methods. These comparisons demonstrate that the simplified method significantly overestimated reinforcement loads, whereas the K-stiffness method provided estimates that were judged to be in better agreement with the measured results. The paper also quantifies the influence of construction procedures on reinforcement strains and load, shows that long-term creep of the reinforcement after 2 years after construction is negligible, and identifies lessons learned.

Closure to “Assessment of Reinforcement Strains in Very Tall Mechanically Stabilized Earth Walls” by Armin W. Stuedlein, Tony M. Allen, Robert D. Holtz, and Barry R. Christopher

In the course of analyzing data collected from two exceptionally tall mechanically stabilized earth (MSE) walls constructed for the third runway at Seattle-Tacoma International Airport (SeaTac), the authors failed to understand three fundamental points regarding MSE wall design: 1. The authors ignore both the mandated design friction angle and the fact that the actual backfill internal friction angle was not known when the wall was designed. Instead, they assess the accuracy of the MSE design methods using selected in-place values of the soil friction angle, 40 and 44 , which are substantially higher than the mandated design friction angle, 37 . 2. The authors also ignore the fact that MSE walls are designed for the finished condition, not for the partially constructed condition. Instead, they condemn the validity of the Coherent Gravity and Simplified design methods based on those methods’ underprediction of reinforcement loads at intermediate stages of construction. Postconstruction stresses in the soil reinforcements at SeaTac are consistent with those predicted by the Coherent Gravity and Simplified methods using the mandated design friction angle, 37 . 3. The earth pressure distribution behind an MSE wall is triangular, not trapezoidal as assumed by the K-Stiffness method.

Design and Performance of 6.3-m-High, Block-Faced Geogrid Wall Designed Using K-Stiffness Method

AbstractA high-density polyethylene (HDPE) geogrid soil-reinforced dry-cast concrete block retaining wall 6.3-m high was designed using the K-stiffness method as part of a highway-widening project southeast of Seattle, Washington. The amount of reinforcement needed for the original wall design using the K-stiffness method was approximately 50% of that required using the AASHTO simplified method. This paper describes the construction, instrumentation program, and interpretation of the measurements. Geogrid strains were measured using strain gauges and extensometers attached to reinforcement layers. An extensive materials testing program was conducted to characterize the backfill soil properties and geogrid stiffness properties and to calibrate strain gauge readings. The reinforcement loads deduced from the measured strains are compared with Class A, B, and C1 predictions using the AASHTO simplified and K-stiffness methods. These comparisons demonstrate that the simplified method significantly overestimated...

Modification of K-stiffness method for MSE structures on soft ground

ABSTRACT: In this paper, a modification of the K-stiffness method, which is used to calculate the reinforcement load of mechanically stabilised earth (MSE) structures on firm foundations, was investigated for application to reinforced structures on soft ground. Current design methods for the estimation of reinforcement loads of reinforced structures on firm foundation, namely the tieback wedge or simplified method, the FHWA structure stiffness method, the original K-stiffness method and the modified K-stiffness method, were applied to calculate the reinforcement loads of two embankments constructed on soft Bangkok clay. From comparisons of the calculated and observed values, a modification of the original K-stiffness method was proposed by suggesting a uniform distribution of the reinforcement loads, and adding one more factor, the settlement factor Φs, to take into account the influence of settlement on the reinforcement loads.

Influence of toe restraint on reinforced soil segmental walls

A verified fast Lagrangian analysis of continua (FLAC) numerical model is used to investigate the influence of horizontal toe stiffness on the performance of reinforced soil segmental retaining walls under working stress (operational) conditions. Results of full-scale shear testing of the interface between the bottom of a typical modular block and concrete or crushed stone levelling pads are used to back-calculate toe stiffness values. The results of numerical simulations demonstrate that toe resistance at the base of a reinforced soil segmental retaining wall can generate a significant portion of the resistance to horizontal earth loads in these systems. This partially explains why reinforcement loads under working stress conditions are typically overestimated using current limit equilibrium-based design methods. Other parameters investigated are wall height, interface shear stiffness between blocks, wall facing batter, reinforcement stiffness, and reinforcement spacing. Computed reinforcement loads are compared with predicted loads using the empirical-based K-stiffness method. The K-stiffness method predictions are shown to better capture the qualitative trends in numerical results and be quantitatively more accurate compared with the AASHTO simplified method.

Influence of reinforcement stiffness and compaction on the performance of four geosynthetic-reinforced soil walls

The paper describes measurements taken from a series of four full-scale modular block walls that were constructed with reinforcement layers having different stiffness. The walls were 3.6 m high and were reinforced with two different polypropylene geogrid reinforcement materials, a polyester geogrid and a welded wire mesh. Each wall was constructed with the same modular block facing and reinforcement spacing of 0.6 m. The influence of compaction effort on wall displacements and horizontal toe load measurements at the end of construction was detectable in this investigation. These values were adjusted to account for the influence of different compaction methods on end-of-construction wall response. However, during subsequent surcharging the effects of initial compaction effort were erased. Reinforcement loads are computed from strain readings and results of in-isolation constant-load (creep) tests. Computed maximum reinforcement loads are compared with values predicted using the current AASHTO Simplified Method and the K-stiffness Method. The predicted magnitude and distribution of reinforcement loads are shown to be more accurate using the K-stiffness Method for polymeric reinforcement materials. For the relatively stiff welded wire mesh product, the measured reinforcement loads fell between values predicted using both methods.

Refinement of K-stiffness Method for geosynthetic-reinforced soil walls

The K-stiffness Method is an empirically-developed working stress method used to compute reinforcement loads for the internal stability design of geosynthetic-reinforced soil walls under serviceability conditions. In this paper, additional data from Japanese case studies for five full-scale field and three full-scale laboratory geosynthetic-reinforced soil walls are added to the database that was used to calibrate the original K-stiffness Method. One more case study from an instrumented wall in the USA is also introduced. Measured loads are compared with predicted loads using the current AASHTO Simplified Method and a modified version of the K-stiffness Method that has been adjusted by back-fitting model parameters to the extended database. The AASHTO Simplified Method is shown to be excessively conservative (on average) with respect to accurate prediction of reinforcement loads and to correlate poorly with measured values. The modified K-stiffness Method is demonstrated by statistical analysis to give ratios (bias) of average measured to predicted reinforcement load values close to 1 and coefficient of variation (COV) values for the maximum reinforcement load in a wall that are less than 25%.

Development of the K-stiffness method for geosynthetic reinforced soil walls constructed with c-ϕ soils

In this paper the K-stiffness method is extended to the case of c-ϕ soils using data obtained from a total of nine new case studies – six from Japan and three from the USA. A common feature in this new data set is that the walls were all constructed with a vertical face using backfill soils with a range of fines content. The walls varied widely with respect to facing type. This new data set together with previously published data for vertical walls is now used to isolate the effect of soil cohesion on reinforcement loads within the framework of the original K-stiffness method. The new data set is used to calibrate a modified K-stiffness method equation that includes a cohesion influence factor. The modified K-stiffness method is demonstrated to quantitatively improve the estimate of the magnitude and distribution of reinforcement loads for internal stability design of vertical-faced geosynthetic reinforced soil walls with c-ϕ soil backfills when compared to the current American Association of State Highway and Transportation Officials simplified method.

Evaluation of K-Stiffness Method for Vertical Geosynthetic Reinforced Granular Soil Walls in Japan

In this paper the K-stiffness Method as originally proposed by Allen et al. (2003) is re-examined using a total of six new case studies-five from Japan and one from the USA. A common feature of the walls in this new data set is that the walls were all constructed with a vertical face and a granular backfill. However, the walls varied widely with respect to facing type. This new data set together with data for vertical walls previously published by Allen and Bathurst (2002a,b) and Allen et al. (2002) is now used to isolate the effect of the facing stiffness factor on reinforcement loads and to adjust the original equation that was developed to calculate its value. The paper also shows that predicted reinforcement loads using the current AASHTO Simplified Method in the USA and the current PWRC method in Japan give the same reinforcement load predictions, and both grossly over-estimate the values deduced from measured strains. The new data set is used to slightly refine the estimate of the facing stiffness factor used in the original K-stiffness Method. The original and modified K-stiffness Method are demonstrated to quantitatively improve the estimate of the magnitude and distribution of reinforcement loads for internal stability design of vertical-faced geosynthetic reinforced soils walls with granular backfills when compared to the current American and Japanese methods.

Field monitoring evaluation of geotextile-reinforced soil-retaining walls

The use of geotextiles as reinforcement in soil-retaining walls may offer benefits over the use of other types of reinforcement, such as metallic strips or geogrids. These include ease of construction, expediency, and significant cost reduction. However, the lack of field monitoring results documenting the behavior of geotextile-reinforced structures, mainly regarding deformations, has precluded widespread utilization of these systems. A better understanding of the behavior of geotextile-reinforced soil structures could be gained by systematic monitoring of full-scale structures, combined with a thorough material characterization program. Accordingly, eight prototype geotextile-reinforced soil structures were built as part of a comprehensive study aimed at analyzing their behavior. This paper presents the characteristics of the prototype wall used as baseline for this series of structures, including construction details, instrumentation layout, and the results of laboratory tests conducted to characterize the soils and geosynthetics involved in this structure. The lateral displacements at the face of the wall were small, with increasing lateral displacements observed over time, particularly in association with precipitation events during the summer season in Brazil. The largest horizontal strains occurred towards the face, at mid-height of the prototype wall. The use of sigmoid curves to fit displacement results within the geotextiles was found to be very useful to define the value and the location of the peak strain in each reinforcement layer. The location of maximum reinforcement strains within each layer was found to be consistent with the development of a potential failure surface starting at the toe of the wall and propagating into the soil mass. The maximum reinforcement tension predicted using the K-stiffness method was found to compare well with reinforcement tension values obtained from monitoring results.

New Method for Prediction of Loads in Steel Reinforced Soil Walls

The paper describes a new working stress design methodology introduced by the writers for geosynthetic reinforced soil walls (K-Stiffness Method) that is now extended to steel reinforced soil walls. A large database of full-scale steel reinforced soil walls (a total of 20 fully instrumented wall sections) was used to develop the new design methodology. The effects of global wall stiffness, soil strength, reinforcement layer spacing, and wall height were investigated. Results of simple statistical analyses using the ratio of measured to predicted peak reinforcement loads (i.e., method bias) demonstrate the improved prediction accuracy. The AASHTO Simplified Method results in an average method bias of 1.1 with a coefficient of variation (COV) of 45%, whereas the proposed K-Stiffness Method results in an average bias of 0.95 and a COV of 32%. Soil strength was found to have limited influence on reinforcement loads for steel reinforced soil walls, especially for high shear strength soils, while global wall stiffness and wall height had a major influence on reinforcement loads.

A new working stress method for prediction of reinforcement loads in geosynthetic walls

Proper estimation of soil reinforcement loads and strains is key to accurate internal stability design of reinforced soil structures. Current design methodologies use limit equilibrium concepts to estimate reinforcement loads for internal stability design of geosynthetic and steel reinforced soil walls. For geosynthetic walls, however, it appears that these methods are excessively conservative based on the performance of geosynthetic walls to date. This paper presents a new method, called the K-stiffness method, that is shown to give more accurate estimates of reinforcement loads, thereby reducing reinforcement quantities and improving the economy of geosynthetic walls. The paper is focused on the new method as it applies to geosynthetic walls constructed with granular (noncohesive, relatively low silt content) backfill soils. A database of 11 full-scale geosynthetic walls was used to develop the new design methodology based on working stress principles. The method considers the stiffness of the various wall components and their influence on reinforcement loads. Results of simple statistical analyses show that the current American Association of State Highway and Transportation Officials (AASHTO) Simplified Method results in an average ratio of measured to predicted loads (bias) of 0.45, with a coefficient of variation (COV) of 91%, whereas the proposed method results in an average bias of 0.99 and a COV of 36%. A principle objective of the method is to design the wall reinforcement so that the soil within the wall backfill is prevented from reaching a state of failure, consistent with the notion of working stress conditions. This concept represents a new approach for internal stability design of geosynthetic-reinforced soil walls because prevention of soil failure as a limit state is considered in addition to the current practice of preventing reinforcement rupture.Key words: geosynthetics, reinforcement, walls, loads, strains, design, K-stiffness method.